Eight Standard >> Ratio and Proportion | Ratio

Ratio:
   It is a relation between the magnitudes of quantities (which can be measured) of the same kind.
   Ex: \(\frac{Rs 2}{50p}=\frac{200p}{50p}=\frac{4}{1}\)

It expresses what multiple or part or parts of the first quantity is the 2nd.

   The ratio has no unit.

Illustration 1: Ratio of Rs 16 and Rs 20

   \(\frac{Rs 16}{Rs 20}=\frac{16}{20}=\frac{4}{5}=4:5\)

Illustration 2: Ratio of 500gm to 2 kgs
      \(\frac{500 gm}{2 kgs}\)= \(\frac{500 gm}{2000 gm}\)= \(\frac{1}{4}\)=\(1:4\)

Rule (A): We can compare two quantities of the same kind but can not compare two dissimilar quantities.

Rule (B): A ratio remains unaltered if its numerator and denominator are multiplied or divided b the same non-zero real number.

    i) \(\frac{ma}{mb}\)=\(\frac{a}{b}\)
    ii) \(\frac{\frac{a}{m}}{\frac{b}{m}}\)=\(\frac{a}{b}\)

     4:3=\(\frac{4}{3}\)=\(\frac{4 \times 5}{3 \times 5}\)=\(\frac{20}{15}\)
    \(\frac{4}{3}\)

    \(\Rightarrow\ 4:3 \equiv 20:15\)